This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A055843 #19 Feb 17 2023 10:04:22
%S A055843 1,13,85,385,1375,4147,11011,26455,58630,121550,238238,445094,797810,
%T A055843 1379210,2309450,3759074,5965487,9253475,14060475,20967375,30735705,
%U A055843 44352165,63081525,88529025,122713500,168152556,227961228,305965660,406833460,536222500,700950052
%N A055843 Expansion of (1+3*x)/(1-x)^10.
%C A055843 Partial sums of A052181.
%D A055843 Albert H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
%H A055843 G. C. Greubel, <a href="/A055843/b055843.txt">Table of n, a(n) for n = 0..1000</a>
%H A055843 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
%F A055843 a(n) = (4*n+9)*binomial(n+8, 8)/9.
%F A055843 G.f.: (1+3*x)/(1-x)^10.
%F A055843 a(n) = 4*binomial(n+9,9) - 3*binomial(n+8,8). - _G. C. Greubel_, Jan 21 2020
%F A055843 Sum_{n>=0} 1/a(n) = 9437184*Pi/24035 + 56623104*log(2)/24035 - 482087736/168245. - _Amiram Eldar_, Feb 17 2023
%p A055843 seq( (4*n+9)*binomial(n+8, 8)/9, n=0..30); # _G. C. Greubel_, Jan 21 2020
%t A055843 Table[4*Binomial[n+9,9] - 3*Binomial[n+8,8], {n,0,30}] (* _G. C. Greubel_, Jan 21 2020 *)
%o A055843 (PARI) vector(31, n, (4*n+5)*binomial(n+7, 8)/9) \\ _G. C. Greubel_, Jan 21 2020
%o A055843 (Magma) [(4*n+9)*Binomial(n+8, 8)/9: n in [0..30]]; // _G. C. Greubel_, Jan 21 2020
%o A055843 (Sage) [(4*n+9)*binomial(n+8, 8)/9 for n in (0..30)] # _G. C. Greubel_, Jan 21 2020
%o A055843 (GAP) List([0..30], n-> (4*n+9)*Binomial(n+8, 8)/9 ); # _G. C. Greubel_, Jan 21 2020
%Y A055843 Cf. A052181.
%Y A055843 Cf. A093561 ((4, 1) Pascal, column m=9).
%K A055843 easy,nonn
%O A055843 0,2
%A A055843 _Barry E. Williams_, May 30 2000